There have been developments of a travel assist apparatus for avoiding collision between a vehicle and a collision avoidance object such as a preceding vehicle present ahead of the first vehicle in a traveling direction. In the above-described device, a speed reduction distance, which is an estimated value of travel distance necessary for stopping the vehicle on the assumption that speed-reduction control for reducing the speed of the vehicle is started at the current time point, is compared with a relative distance between the host vehicle and the collision avoidance object measured by a radar installed in the host vehicle. Then, when the thus detected latest relative distance is equal to or less than an addition value obtained by adding a specified distance (greater than 0 (zero)) to the speed reduction distance, the speed-reduction control is actually started.
A method for calculating the above-described speed reduction distance includes a method for calculation using the relational expression 1 given below (refer to Patent Document 1, for example).R=(VSa2)/(2·a)  (Expression 1)
where R represents speed reduction distance; VSa represents speed of vehicle; a represents estimated deceleration on performance of speed-reduction control